The set of real numbers is denoted by \(\mathbb {R}\) .
The sets of \(n\) -dimensional column-vectors and \(m\) -by-\(n\)  matrices of which elements belong to a set \(X\)  are denoted by \(X^{n}\)  and \(X^{m\times n}\) , respectively.
An algorithm \(\mathcal {A}\)  is polynomial-time algorithm if there exists a polynomial \(p\)  such that, for every \(k\) -bit length input \(x\) , \(\mathcal {A}(x)\)  terminates within at most \(p(k)\)  steps [1]}.
We say a function \(\epsilon :\lbrace 1,2,3,\dots \rbrace \rightarrow \mathbb {R}\)  is negligible if, for every positive integer \(c>0\) , there exists an integer \(N\)  such that \(|\epsilon (n)|<n^{-c}\)  holds for all \(n>N\)  [1]}.
